Effects of nonlocal plasmons in gapped graphene micro-ribbon array and 2DEG on near-field electromagnetic response in the deep-subwavelength regime

TL;DR

This paper develops a comprehensive analytical model to study nonlocal plasmon effects in gapped graphene micro-ribbon arrays coupled with a 2DEG, revealing tunable near-field electromagnetic responses in the deep-subwavelength regime.

Contribution

It introduces a self-consistent analytical framework incorporating nonlocal effects and diffraction modes for graphene micro-ribbons and 2DEG systems, extending beyond the long-wavelength limit.

Findings

Discovery of externally-tunable electromagnetic coupling among surface, electron gas, and graphene plasmons.

Analytical expressions for optical-response functions including non-locality.

Comparison with experimental data on graphene plasmon energies.

Abstract

A self-consistent theory involving Maxwell equations and a density-matrix linear-response theory is solved for an electromagnetically-coupled doped graphene micro-ribbon array and a quantum-well electron gas sitting at an interface between a half-space of air and another half-space of a doped semiconductor substrate which supports a surface-plasmon mode in our system. The coupling between a spatially-modulated total electromagnetic field and the electron dynamics in a Dirac-cone of a graphene ribbon, as well as the coupling of the far-field specular and near-field higher-order diffraction modes, are included in the derived electron optical-response function. Full analytical expressions are obtained with non-locality for the optical-response functions of a two-dimensional electron gas and a graphene layer with an induced bandgap, and are employed in our numerical calculations beyond the long-wavelength limit (Drude model). Both the near-field transmissivity and reflectivity spectra, as well as their dependence on different configurations of our system and on the array period, ribbon width, graphene chemical potential of quantum-well electron gas and bandgap in graphene, are studied. Moreover, the transmitted E-field intensity distribution is calculated to demonstrate its connection to the mixing of specular and diffraction modes of the total electromagnetic field. An externally-tunable electromagnetic coupling among the surface, conventional electron-gas and massless graphene intraband plasmon excitations is discovered and explained. Furthermore, a comparison is made between the dependence of the graphene-plasmon energy on the ribbon width and chemical potential in this paper and the recent experimental observation given by Ju, et al., [Nature Nanotechnology, 6, 630 (2011)] for a graphene micro-ribbon array in the terahertz-frequency range.